Sure, but then maybe don't call it "public" as people will think it can be downloaded without creating an account. Calling something public but require account creation is misleading.
Radio is free, but you hear advertisements. Probably better to create an account than to have product placement in the actual data.
Not sure were you are from, but where I'm from (Sweden), public radio (not free but public) and public TV is free of advertisement and does not require me to sign up for an account to be able to listen to/watch it. That's what I call public.
For example, the government where I live (Catalunya) has public data. So I can go to the website and click download, no account required. If that data was distributed via Kaggle and requires account signup to get, I would not consider what they are providing public.